数学最新文献

{"title":"Repeated-root constacyclic codes of length kslmpn over finite fields","authors":"Qi Zhang ,&nbsp;Weiqiong Wang ,&nbsp;Shuyu Luo ,&nbsp;Yue Li","doi":"10.1016/j.ffa.2024.102542","DOIUrl":"10.1016/j.ffa.2024.102542","url":null,"abstract":"<div><div>For different odd primes <em>k</em>, <em>l</em>, <em>p</em>, and positive integers <em>s</em>, <em>m</em>, <em>n</em>, the polynomial <span><math><msup><mrow><mi>x</mi></mrow><mrow><msup><mrow><mi>k</mi></mrow><mrow><mi>s</mi></mrow></msup><msup><mrow><mi>l</mi></mrow><mrow><mi>m</mi></mrow></msup><msup><mrow><mi>p</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow></msup><mo>−</mo><mi>λ</mi></math></span> in <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow></msub><mrow><mo>[</mo><mi>x</mi><mo>]</mo></mrow></math></span> is explicitly factorized, where <em>p</em> is the characteristic of <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow></msub></math></span>, <span><math><mi>λ</mi><mo>∈</mo><msubsup><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup></math></span>. All repeated-root constacyclic codes and their dual codes of length <span><math><msup><mrow><mi>k</mi></mrow><mrow><mi>s</mi></mrow></msup><msup><mrow><mi>l</mi></mrow><mrow><mi>m</mi></mrow></msup><msup><mrow><mi>p</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> over <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow></msub></math></span> are characterized. In addition, the characterization and enumeration of all linear complementary dual (LCD) cyclic and negacyclic codes of length <span><math><msup><mrow><mi>k</mi></mrow><mrow><mi>s</mi></mrow></msup><msup><mrow><mi>l</mi></mrow><mrow><mi>m</mi></mrow></msup><msup><mrow><mi>p</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> over <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow></msub></math></span> are obtained.</div></div>","PeriodicalId":50446,"journal":{"name":"Finite Fields and Their Applications","volume":"101 ","pages":"Article 102542"},"PeriodicalIF":1.2,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142660203","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the Emden-Fowler equation type involving double critical growth","authors":"Luiz Fernando de Oliveira Faria ,&nbsp;Aldo Henrique de Souza Medeiros ,&nbsp;Jeferson Camilo Silva","doi":"10.1016/j.jde.2024.11.011","DOIUrl":"10.1016/j.jde.2024.11.011","url":null,"abstract":"<div><div>In this article, we investigate a class of nonlinear elliptic equations driven by the <em>p</em>-Laplacian operator in the entire space <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span>, known as the Emden-Fowler equation type. The complexity of the problem arises from the interplay of two distinct critical growth phenomena, characterized by both Sobolev and Hardy senses. We explore the existence of positive radial solutions, with the proof relying on variational methods. Due to multiple critical nonlinearities, the Mountain Pass Lemma does not yield critical points but only Palais-Smale sequences. The primary challenge lies in the asymptotic competition among the energies carried by these multiple critical nonlinearities.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"416 ","pages":"Pages 1861-1880"},"PeriodicalIF":2.4,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142652792","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global classical solutions of free boundary problem of compressible Navier–Stokes equations with degenerate viscosity","authors":"Andrew Yang ,&nbsp;Xu Zhao ,&nbsp;Wenshu Zhou","doi":"10.1016/j.jde.2024.11.004","DOIUrl":"10.1016/j.jde.2024.11.004","url":null,"abstract":"<div><div>This paper concerns with the one dimensional compressible isentropic Navier–Stokes equations with a free boundary separating fluid and vacuum when the viscosity coefficient depends on the density. Precisely, the pressure <em>P</em> and the viscosity coefficient <em>μ</em> are assumed to be proportional to <span><math><msup><mrow><mi>ρ</mi></mrow><mrow><mi>γ</mi></mrow></msup></math></span> and <span><math><msup><mrow><mi>ρ</mi></mrow><mrow><mi>θ</mi></mrow></msup></math></span> respectively, where <em>ρ</em> is the density, and <em>γ</em> and <em>θ</em> are constants. We establish the unique solvability in the framework of global classical solutions for this problem when <span><math><mi>γ</mi><mo>≥</mo><mi>θ</mi><mo>&gt;</mo><mn>1</mn></math></span>. Since the previous results on this topic are limited to the case when <span><math><mi>θ</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span>, the result in this paper fills in the gap for <span><math><mi>θ</mi><mo>&gt;</mo><mn>1</mn></math></span>. Note that the key estimate is to show that the density has a positive lower bound and the new ingredient of the proof relies on the study of the quasilinear parabolic equation for the viscosity coefficient by reducing the nonlocal terms in order to apply the comparison principle.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"416 ","pages":"Pages 1837-1860"},"PeriodicalIF":2.4,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142652791","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the minimum spectral radius of graphs with given order and dissociation number","authors":"Jing Zhao ,&nbsp;Huiqing Liu ,&nbsp;Jin Xiong","doi":"10.1016/j.dam.2024.11.014","DOIUrl":"10.1016/j.dam.2024.11.014","url":null,"abstract":"<div><div>A dissociation set in a graph <span><math><mi>G</mi></math></span> is a set of vertices that induces a subgraph of maximum degree at most 1. The cardinality of a maximum dissociation set in <span><math><mi>G</mi></math></span> is called the dissociation number of <span><math><mi>G</mi></math></span>. Huang et al. determined the graphs with the minimum spectral radius among all connected graphs with given order <span><math><mi>n</mi></math></span> and dissociation number <span><math><mrow><mn>2</mn><mo>,</mo><mrow><mo>⌈</mo><mfrac><mrow><mn>2</mn><mi>n</mi></mrow><mrow><mn>3</mn></mrow></mfrac><mo>⌉</mo></mrow><mo>,</mo><mi>n</mi><mo>−</mo><mn>2</mn><mo>,</mo><mi>n</mi><mo>−</mo><mn>1</mn></mrow></math></span>, respectively. In this paper, we characterize the graphs that attain the minimum spectral radius among all connected graphs with given order <span><math><mi>n</mi></math></span> and dissociation number <span><math><mrow><mrow><mo>⌈</mo><mfrac><mrow><mn>2</mn><mi>n</mi></mrow><mrow><mn>3</mn></mrow></mfrac><mo>⌉</mo></mrow><mo>−</mo><mn>1</mn></mrow></math></span>.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"361 ","pages":"Pages 487-501"},"PeriodicalIF":1.0,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142650596","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Some Properties on the Reversibility and the Linear Response Theory of Langevin Dynamics","authors":"Yuan Gao,&nbsp;Jian-Guo Liu,&nbsp;Zibu Liu","doi":"10.1007/s10440-024-00702-w","DOIUrl":"10.1007/s10440-024-00702-w","url":null,"abstract":"<div><p>Linear response theory is a fundamental framework studying the macroscopic response of a physical system to an external perturbation. This paper focuses on the rigorous mathematical justification of linear response theory for Langevin dynamics. We give some equivalent characterizations for reversible overdamped/underdamped Langevin dynamics, which is the unperturbed reference system. Then we clarify sufficient conditions for the smoothness and exponential convergence to the invariant measure for the overdamped case. We also clarify those sufficient conditions for the underdamped case, which corresponds to hypoellipticity and hypocoercivity. Based on these, the asymptotic dependence of the response function on the small perturbation is proved in both finite and infinite time horizons. As applications, Green-Kubo relations and linear response theory for a generalized Langevin dynamics are also proved in a rigorous fashion.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"194 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142636905","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A supplement to the large deviations of infinite weighted sums of heavy tailed random variables","authors":"Jianan Shi ,&nbsp;Zhenhong Yu ,&nbsp;Yu Miao","doi":"10.1016/j.spl.2024.110306","DOIUrl":"10.1016/j.spl.2024.110306","url":null,"abstract":"<div><div>Let <span><math><mrow><mo>{</mo><mi>X</mi><mo>,</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>,</mo><mi>n</mi><mo>≥</mo><mn>1</mn><mo>}</mo></mrow></math></span> be a sequence of independent and identically distributed non-negative random variables with heavy tails and <span><math><mrow><mo>{</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>i</mi></mrow></msub><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow><mo>,</mo><mi>i</mi><mo>≥</mo><mn>1</mn><mo>,</mo><mi>n</mi><mo>≥</mo><mn>1</mn><mo>}</mo></mrow></math></span> be an array of non-negative numbers. In the present paper, we study the large deviation of infinite weighted sums <span><math><mrow><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>∞</mi></mrow></msubsup><msub><mrow><mi>a</mi></mrow><mrow><mi>i</mi></mrow></msub><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow><msub><mrow><mi>X</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></math></span>, which is a supplement of Aurzada (2020).</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"217 ","pages":"Article 110306"},"PeriodicalIF":0.9,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142663764","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Complete description of measures corresponding to Abelian varieties over finite fields","authors":"Nikolai S. Nadirashvili ,&nbsp;Michael A. Tsfasman","doi":"10.1016/j.ffa.2024.102543","DOIUrl":"10.1016/j.ffa.2024.102543","url":null,"abstract":"<div><div>We study probability measures corresponding to families of abelian varieties over a finite field. These measures play an important role in the Tsfasman–Vlăduţ theory of asymptotic zeta-functions defining completely the limit zeta-function of the family. J.-P. Serre, using results of R.M. Robinson on conjugate algebraic integers, described the possible set of measures than can correspond to families of abelian varieties over a finite field. The problem whether all such measures actually occur was left open. Moreover, Serre supposed that not all such measures correspond to abelian varieties (for example, the Lebesgue measure on a segment). Here we settle Serre's problem proving that Serre conditions are sufficient, and thus describe completely the set of measures corresponding to abelian varieties.</div></div>","PeriodicalId":50446,"journal":{"name":"Finite Fields and Their Applications","volume":"101 ","pages":"Article 102543"},"PeriodicalIF":1.2,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142660194","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A second-order fitted scheme for time fractional telegraph equations involving weak singularity","authors":"Caixia Ou, Dakang Cen, Zhibo Wang, Seakweng Vong","doi":"10.1007/s13540-024-00355-4","DOIUrl":"https://doi.org/10.1007/s13540-024-00355-4","url":null,"abstract":"<p>In the present paper, to fill the gap of the effect of singularity arising from multiple fractional derivatives on numerical analysis, the regularity and high order difference scheme for time fractional telegraph equations are taken into consideration. Firstly, the analytic solution is obtained by employing Laplace transform, and its regularity is then deduced. Secondly, by the technic of decomposition, the improved regularity of solution is derived. Furthermore, to overcome the weak singularity and enhance convergence precision, a second-order fitted scheme based on <i>L</i>2-<span>(1_sigma )</span> approximation and order reduction method is applied to such problems, which is an improvement for the work [6]. Ultimately, examples are presented to verify the effectiveness of our theoretical results.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"6 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142637871","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A characterization of the Grassmann graphs","authors":"Alexander L. Gavrilyuk ,&nbsp;Jack H. Koolen","doi":"10.1016/j.jctb.2024.11.001","DOIUrl":"10.1016/j.jctb.2024.11.001","url":null,"abstract":"<div><div>The Grassmann graph <span><math><msub><mrow><mi>J</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>(</mo><mi>n</mi><mo>,</mo><mi>D</mi><mo>)</mo></math></span> is a graph on the <em>D</em>-dimensional subspaces of <span><math><msubsup><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow><mrow><mi>n</mi></mrow></msubsup></math></span> with two subspaces being adjacent if their intersection has dimension <span><math><mi>D</mi><mo>−</mo><mn>1</mn></math></span>. Characterizing these graphs by their intersection numbers is an important step towards a solution of the classification problem for <span><math><mo>(</mo><mi>P</mi><mrow><mspace></mspace><mi>and</mi><mspace></mspace></mrow><mi>Q</mi><mo>)</mo></math></span>-polynomial association schemes, posed by Bannai and Ito in their monograph “Algebraic Combinatorics I” (1984).</div><div>Metsch (1995) <span><span>[37]</span></span> showed that the Grassmann graph <span><math><msub><mrow><mi>J</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>(</mo><mi>n</mi><mo>,</mo><mi>D</mi><mo>)</mo></math></span> with <span><math><mi>D</mi><mo>≥</mo><mn>3</mn></math></span> is characterized by its intersection numbers except for the following two principal open cases: <span><math><mi>n</mi><mo>=</mo><mn>2</mn><mi>D</mi></math></span> or <span><math><mi>n</mi><mo>=</mo><mn>2</mn><mi>D</mi><mo>+</mo><mn>1</mn></math></span>. Van Dam and Koolen (2005) <span><span>[57]</span></span> constructed the twisted Grassmann graphs with the same intersection numbers as the Grassmann graphs <span><math><msub><mrow><mi>J</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>(</mo><mn>2</mn><mi>D</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>D</mi><mo>)</mo></math></span> (for any prime power <em>q</em> and <span><math><mi>D</mi><mo>≥</mo><mn>2</mn></math></span>), but not isomorphic to the latter ones. This shows that characterizing the graphs in the remaining cases would require a conceptually new approach.</div><div>We prove that the Grassmann graph <span><math><msub><mrow><mi>J</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>(</mo><mn>2</mn><mi>D</mi><mo>,</mo><mi>D</mi><mo>)</mo></math></span> is characterized by its intersection numbers provided that <em>D</em> is large enough.</div></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"171 ","pages":"Pages 1-27"},"PeriodicalIF":1.2,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142663746","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Frobenius integrability theorem for plane fields generated by quasiconformal deformations","authors":"Slobodan N. Simić","doi":"10.1016/j.difgeo.2024.102202","DOIUrl":"10.1016/j.difgeo.2024.102202","url":null,"abstract":"<div><div>We generalize the classical Frobenius integrability theorem to plane fields of class <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>Q</mi></mrow></msup></math></span>, a regularity class introduced by Reimann <span><span>[9]</span></span> for vector fields in Euclidean spaces. Reimann showed that a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>Q</mi></mrow></msup></math></span> vector field is uniquely integrable and its flow is a quasiconformal deformation. We prove that an a.e. involutive <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>Q</mi></mrow></msup></math></span> plane field (defined in a suitable way) in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> is integrable, with integral manifolds of class <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>Q</mi></mrow></msup></math></span>.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"97 ","pages":"Article 102202"},"PeriodicalIF":0.6,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142660249","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}